8. Introduction to Trigonometry
medium

સાબિત કરો કે $\left(\sin ^{4} \theta-\cos ^{4} \theta+1\right) \operatorname{cosec}^{2} \theta=2$

Option A
Option B
Option C
Option D

Solution

ડા.બા. $=\left(\sin ^{4} \theta-\cos ^{4} \theta+1\right) \operatorname{cosec}^{2} \theta$

$=\left[\left(\sin ^{2} \theta-\cos ^{2} \theta\right)\left(\sin ^{2} \theta+\cos ^{2} \theta\right)+1\right] \operatorname{cosec}^{2} \theta$

$=\left(\sin ^{2} \theta-\cos ^{2} \theta+1\right) \operatorname{cosec}^{2} \theta$

$\quad\left[\right.$  $\left.\sin ^{2} \theta+\cos ^{2} \theta=1\right]$

$=2 \sin ^{2} \theta \operatorname{cosec}^{2} \theta \quad\left[\right.$ $\left.1-\cos ^{2} \theta=\sin ^{2} \theta\right]$

$=2=$ જ.બા.

Standard 10
Mathematics

Similar Questions

Start a Free Trial Now

Confusing about what to choose? Our team will schedule a demo shortly.